The alpha hydrogen of a carbonyl group is relatively acidic and therefore can be deprotonated. This results in a lone pair that resides on the alpha carbon, which can now act as a nucleophile and attack some other electrophile. Also, as you hinted, the carbonyl group carbon is partially positive and therefore a good electrophile. Any good nucleophile can attack at this position. Essentially all you're doing is looking for the electrophile and nuclephile and asking yourself, what typically happens and where.
There is a special scenario when you have a double bond between the alpha beta carbons (for example. an alpha-beta unsaturated ketone). In this instance, because of resonance, there is a partial positive charge that resides on the beta carbon and this too can be attacked by nucleophiles. As it turns out, in this type of scenario, where you have two potentially good electrophiles on a certain molecule, nucleophiles can react selectively for one region vs. the other, but this is not something that's required to know.